190537edo: Difference between revisions
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Created page with "{{Infobox ET}} The '''190537edo''' divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log<sub>2</sub>3 past 1..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
The '''190537edo''' divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log<sub>2</sub>3 past [[111202edo|111202]], before [[10590737edo|10590737]]. Notably, it's the first EDO with a 3-2 [[telicity]] strength greater that 1 since [[665edo]]. | The '''190537edo''' divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log<sub>2</sub>3 past [[111202edo|111202]], before [[10590737edo|10590737]]. Notably, it's the first EDO with a 3-2 [[telicity]] k-strength greater that 1 since [[665edo]] and it even surpasses 665edo in telicity k-strength. | ||
== Theory == | == Theory == | ||
Revision as of 12:32, 22 December 2022
| ← 190536edo | 190537edo | 190538edo → |
(convergent)
The 190537edo divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log23 past 111202, before 10590737. Notably, it's the first EDO with a 3-2 telicity k-strength greater that 1 since 665edo and it even surpasses 665edo in telicity k-strength.
Theory
190537edo has a consistency limit of 11, which is rather impressive for a convergent. However, it's strongest in the 2.3.7.17.23 subgroup.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00000 | -0.00134 | +0.00010 | +0.00175 | +0.00200 | +0.00058 | -0.00230 | +0.00048 | -0.00079 | +0.00187 |
| Relative (%) | +0.0 | +0.0 | -21.3 | +1.5 | +27.8 | +31.7 | +9.3 | -36.5 | +7.6 | -12.5 | +29.8 | |
| Steps (reduced) |
190537 (0) |
301994 (111457) |
442413 (61339) |
534905 (153831) |
659150 (87539) |
705071 (133460) |
778813 (16665) |
809387 (47239) |
861906 (99758) |
925625 (163477) |
943958 (181810) | |